Robotic force/torque sensor with improved temperature compensation

ABSTRACT

Strain gages on a robotic force/torque sensor are individually temperature compensated prior to resolving the gage outputs to estimate force and torque loads on the sensor. Thermal sensors are mounted proximate each strain gage, and the initial gate and thermal sensor outputs at a known load and temperature are obtained. The force/torque sensor then undergoes warming, and strain gage and thermal sensor outputs are again obtained. These gage and thermal sensor outputs are processed to calculate coefficients to a temperature compensation equation, such as by using a least squares algorithm. Each strain gage output is compensated using the temperature compensation equation, and the temperature-compensated outputs of the strain gages are then combined to resolve temperature-compensated force and torque values.

FIELD OF INVENTION

The present invention relates generally to a force/torque sensor forrobotic applications, and in particular to thermal compensation ofstrain gages on the robotic force/torque sensor.

BACKGROUND

Robotics is a growing, and increasingly important, field in industrial,medical, scientific, and other applications. In many cases, in which arobot arm or a tool attached thereto contacts a workpiece, the forceand/or torque applied must be closely monitored. Accordingly, aforce/torque sensor is an important part of many robotic systems.

One conventional type of force/torque sensor uses strain gages tomeasure the deformation of small beams connecting two mechanicalparts—one connected to the robot arm and the other connected to arobotic tool (or a mechanical coupling to the tool). For example, acentral “hub,” referred to in the art as a Tool Adapter Plate (TAP) isconnected to a tool. Another body arranged annularly around, and spacedapart from, the TAP, referred to in the art as a Mounting Adapter Plate(MAP), is connected to a robotic arm. The MAP and TAP are connected toeach other by a plurality of relatively thin (and hence mechanicallydeformable) beams, arranged radially around the TAP—in some casesresembling spokes of a wheel. Relative force or torque between objectsrespectively attached to the TAP and MAP attempt to move the MAPrelative to the TAP, resulting in slight deformation, or bending, of atleast some of the beams.

Strain gages affixed to some or all surfaces of each beam generate anelectrical signal proportional to the deformation experienced by thebeam. By resolving the magnitudes of strain gage outputs and noting thelocations of the gages, the strain of the beams may be quantified, andforces and torques induced between the TAP and MAP may be estimated.Numerous types of strain gages, various configurations for locatingstrain gages on beam surfaces, different topologies interconnectingstrain gages, and different means of calibrating their outputs are knownin the art.

A primary source of error in robotic force/torque sensors is inaccuracydue to thermal drift. Sources of thermal drift include ambienttemperature change, ambient temperature gradients, and self-heating. Forsilicon strain gages, changes in output voltage due to temperaturechange can be several times the magnitude of output voltage changes dueto induced stresses—the devices may be considered to be bettertemperature sensors than stress sensors. Connecting strain gages in ahalf-bridge topology can compensate for temperature effects, but only ifthe gages are well matched and only if they are place precisely oppositeeach other. Furthermore, in addition to affecting strain gage output,temperature changes in a robotic force-torque sensor can inducemechanical stresses due to unequal expansion/compression of structuralelements, which the sensor may interpret as an applied load or force.Understanding and compensating temperature error stands as a primarychallenge to robotic force/torque sensor design and operation.

The Background section of this document is provided to place embodimentsof the present invention in technological and operational context, toassist those of skill in the art in understanding their scope andutility. Unless explicitly identified as such, no statement herein isadmitted to be prior art merely by its inclusion in the Backgroundsection.

SUMMARY

The following presents a simplified summary of the disclosure in orderto provide a basic understanding to those of skill in the art. Thissummary is not an extensive overview of the disclosure and is notintended to identify key/critical elements of embodiments of theinvention or to delineate the scope of the invention. The sole purposeof this summary is to present some concepts disclosed herein in asimplified form as a prelude to the more detailed description that ispresented later.

According to one or more embodiments described and claimed herein,strain gages on a robotic force/torque sensor are individuallytemperature compensated prior to resolving the gage outputs to estimateforce and torque loads on the sensor. Thermal sensors are mountedproximate each strain gage, and the initial gage and thermal sensoroutputs at a known load and temperature are obtained. The force/torquesensor then undergoes warming, and strain gage and thermal sensoroutputs are again obtained. These gage and thermal sensor outputs areprocessed to calculate coefficients to a temperature compensationequation, such as by using a least squares algorithm. Each strain gageoutput is compensated using the temperature compensation equation, andthe temperature-compensated outputs of the strain gages are thencombined to resolve temperature-compensated force and torque values.

One embodiment relates to a temperature-compensated method of operatinga robotic force/torque sensor. The robotic force/torque sensor includesa Tool Adapter Plate (TAP) operative to be connected to a first objectand a Mounting Adapter Plate (MAP) operative to be connected to a secondobject. The force/torque sensor is operative to measure the directionand magnitude of force and torque between the first and second objects.Initial outputs of strain gages affixed to members connecting the MAPand TAP, and thermal sensors measuring the temperature of the MAP andTAP, are obtained at a known load and temperature. Strain gage andthermal sensor outputs are obtained after the sensor undergoes atemperature change. Coefficients to a per-gage temperature compensationequation are calculated based on the initial outputs and outputs afterthe temperature change. Each strain gage output is compensated using thetemperature compensation equation. The temperature-compensated outputsof all strain gages are combined to resolve temperature-compensatedforce and torque values.

Another embodiment relates to a temperature-compensated roboticforce/torque sensor. The robotic force/torque sensor includes a ToolAdapter Plate (TAP) operative to be connected to a first object; aMounting Adapter Plate (MAP) operative to be connected to a secondobject; one or more deformable beams connecting the TAP to the MAP; atleast one strain gage affixed to at least one side of each beam, thestrain gages operative to transduce tensile and compressive forces on asurface of a side of a beam, caused by deformation of the beam, intoelectrical signals; a first thermal sensor affixed to the TAP; a secondthermal sensor affixed to the MAP; and a measurement circuit operativeto measure, in response to electrical signals from all strain gages andtemperature outputs from all thermal sensors, thetemperature-compensated direction and magnitude of force and torquebetween the first and second objects.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will now be described more fully hereinafter withreference to the accompanying drawings, in which embodiments of theinvention are shown. However, this invention should not be construed aslimited to the embodiments set forth herein. Rather, these embodimentsare provided so that this disclosure will be thorough and complete, andwill fully convey the scope of the invention to those skilled in theart. Like numbers refer to like elements throughout.

FIG. 1 is a section diagram of one means of mounting a surface-mountthermistor.

FIG. 2 is a schematic circuit diagram of quarter bridge sensor topologymeasurement.

FIG. 3 is a schematic circuit diagram of voltage and current in a bridgecircuit.

FIG. 4 is a graph of worst case min/max temperature errors for ahalf-bridge circuit topology calculated from the bridge currentmeasurement.

FIG. 5 depicts thermal sensor placement on a robotic force/torquesensor.

FIG. 6 is a graph of uncompensated force and torque readings.

FIG. 7 is a graph of the force and torque readings of FIG. 5 aftertemperature compensation.

FIGS. 8A-8C are graphs of force/torque resolution for a roboticforce/torque sensor under various conditions of heating and loading,using no temperature compensation (8A), unstressed strain gage outputcompensation (8B), and per-strain gage temperature compensation (8C).

FIG. 9 is a section perspective view of a robotic force/torque sensorshowing an unstrained member or the mounting of a temperaturecompensation strain gage.

FIG. 10 is a flow diagram of a method of operating a roboticforce/torque sensor.

DETAILED DESCRIPTION

For simplicity and illustrative purposes, the present invention isdescribed by referring mainly to an exemplary embodiment thereof. In thefollowing description, numerous specific details are set forth in orderto provide a thorough understanding of the present invention. However,it will be readily apparent to one of ordinary skill in the art that thepresent invention may be practiced without limitation to these specificdetails. In this description, well known methods and structures have notbeen described in detail so as not to unnecessarily obscure the presentinvention.

Sources of Thermal Error

It is known in the art that temperature drift is a major source ofinaccuracy in robotic force/torque sensors. The inventors haveidentified four major sources of temperature error.

First, the use of silicon strain gages introduces thermal errors.Silicon strain gages are preferred due to their high sensitivity,compared to foil strain gages. However, they exhibit significantly worsetemperature performance. There are two main temperature effects insilicon strain gages—strain gage Temperature Coefficient of Resistance(TCR) and strain gage Temperature Coefficient of Gage Factor (TCGF). TCRarises as the resistance of a silicon strain gage changes with itstemperature. In some gages, resistance can change more over a 0-50° C.temperature swing than it changes due to full scale sensor loading. Muchof this temperature variation can be cancelled by wiring the straingages in a half-bridge configuration; however there is always somemismatch which affects performance. TCGF arises as the gage factor (alsoknown as sensitivity or gain) of a silicon gage changes significantlyover temperature.

Second, the particular force/torque sensor design utilized fortemperature investigation and compensation is susceptible to unequalexpansion and contraction of metals. The most significant errorresulting from sensor design is a force output on the Z-axis caused bydifferent expansion rates between the body of the transducer and MAP orTAP, or a temperature gradient between the MAP and TAP. Other mechanicalissues may additionally contribute to thermal error, but this is by farthe worst.

Third, a temperature gradient across a strain gage bridge will causeeach gage in, e.g., a half-bridge circuit, to be at a differenttemperature. This will cause a significant bridge output due to thesilicon strain gage's large temperature coefficient. This problem islargely alleviated in a quarter-bridge topology.

Finally, electronics can introduce offset error over temperature; gainerror over temperature; and low frequency noise that looks liketemperature error. Electronics integrated into a sensor will also causea significant amount of self-heating that causes or exacerbates theabove temperature errors.

According to embodiments of the present invention, thermal sensors areaffixed to a force/torque sensor in order to allow for temperaturecompensation of strain gage outputs. In general, the term “thermalsensor” is to be construed broadly.

Types of Thermal Sensors

In one embodiment, a thermal sensor may comprise a strain gage, of thesame type and size as the strain gages used to measure mechanicalforces, affixed to an unstressed member of the force/torque sensor. Asused herein, such a thermal sensor is referred to as an “unstressedstrain gage,” or a “thermal strain gage.” In contrast, the strain gagesaffixed to deformable beams of the force/torque sensor—the outputs ofwhich are used to measure forces and torques applied to the sensor—arereferred to herein as “measurement strain gages,” or simply “straingages.”

As mentioned in the background, the outputs of silicon strain gages, inparticular, are known to vary widely over temperature, independently ofthe mechanical strain the gage is employed to measure. The advantages ofusing an unstressed strain gage as a thermal sensor include a repeatableand substantially linear thermal response. Additionally, the unstressedstrain gage may utilize the same installation process as the measurementstrain gages, and will mimic the self-heating characteristics of themeasurement strain gages. A disadvantage to this approach is that theunstressed strain gage is, of course, sensitive to strain. Accordingly,it should be affixed to a member or element of the force/torque sensorthat is not stressed by the forces and torques encountered by elementsto which the measurement strain gages are affixed. This means theunstressed strain gage usually cannot be located proximate to themeasurement strain gages, and hence its temperature output may notaccurately reflect the measurement strain gage temperatures.Furthermore, even when affixed to an unstressed member, the unstressedstrain gage may experience strain as the element to which it is affixedexpands or contracts in response to changes in temperature. Accordingly,applications with wide, rapid changes in sensor temperature may mitigateagainst use of an unstressed strain gage as a thermal sensor.

Another possible implementation of a thermal sensor is a thermocouple—ajunction of two dissimilar conductors that produces atemperature-dependent voltage between them as a result of thethermoelectric effect. Thermocouples can be very small, and are easilyinstalled (no electrical insulation is required). They have a very widetemperature operating range, and very fast response times. On the otherhand, thermocouples have relatively low resolution, accuracy, andrepeatability. More circuitry is required, such as on an interfaceboard, to read thermocouples, as compared to resistive temperaturesensors. Due to their low resolution, the use of thermocouples asthermal sensors on a force/torque sensor would negatively impactresolved force/torque sensor resolution. Accordingly, they are not agood choice for this application.

Resistance Temperature Detectors (RTD) are thermal sensors, typicallycomprising fine wire of pure material (e.g., platinum, nickel, orcopper) wrapped around a ceramic or glass core. The RTD has an accurateresistance/temperature relationship, which can be exploited to measuretemperature. Their response is very linear, having excellentrepeatability and accuracy. Very simple math may be used to obtain alinear reading, operating over a wide temperature range. RTDs have arelatively small signal output, and are generally larger and moreexpensive than other types of thermal sensors, such as thermistors.Furthermore, RTDs can be sensitive to strain, which is problematic inattempting to monitor the temperature of, or near, measurement straingages. RTDs may be particularly suitable in applications outside of therange −20° C. to +60° C. Otherwise, the low resolution and potentialstrain sensitivity make them ill-suited for use as thermal sensors onforce/torque sensors.

A thermistor is a type of resistor for which electrical resistance ishighly dependent on temperature. Thermistors have very high temperaturesensitivity, with low sensitivity to vibration or stress. Thesecharacteristics, along with good repeatability and accuracy, and wideavailability in inexpensive, small packages, make thermistors agenerally good choice for thermal sensors on a force/torque sensor.Thermistors do have an exponential resistance characteristic, whichrequires extensive mathematical processing or lookup tables to linearizetheir readings. In addition, they can be too sensitive for very widetemperature ranges. Overall, the high resolution of thermistors ensuresthe temperature compensation will not negatively impact resolvedforce/torque resolution, making them a good choice for temperaturecompensation of a force/torque sensor, at least over a moderatetemperature range (e.g., −20° C. to +60° C.).

Another possible thermal sensor is an active sensor integrated circuit,such as the Texas Instruments LMT70A. This sensor provides a highlyaccurate and linear temperature output, with high resolution. However,it must be installed on a printed circuit board, and requires a fairlystrict power supply voltage range. In applications where the requirementof a PCB is not problematic, an active sensor provides good results, andremoves the need to linearize the thermal sensors.

A remote Infra-Red (IR) sensor, in some applications, can provideaccurate temperature readings without requiring physical contact andhence manual wiring. One example is the Texas Instruments TMP006 IRthermopile contactless temperature sensor. However, it can be difficultto measure specific point temperatures due to the IR viewing angle.Additionally, the resolution of measurement may be inadequate fortemperature compensation in a force/torque sensor application. Somemeasures may increase the suitability of an IR thermal sensor, such ascoating at least some of the force/torque sensor body with a materialthat mimics a black body.

Thermal Sensor Mounting

Temperature sensors may be mounted to a force/torque sensor in a varietyof ways. Wired temperature sensors may be mounted to a sensor body,using thermal transfer tape or epoxy. Surface mount temperature sensorsmay be mounted to a sensor body, using spacers or within a recess.

A wired temperature sensor can be mounted to the force/torque sensorbody using thermal transfer tape. One suitable tape is 1/2-5-8810,available from 3M Company of Maplewood, Minn. The tape can be placed onthe F/T sensor body where the temperature sensor is to be mounted, andthen the wired sensor can be pressed into the tape so that it is held inplace. The thermal transfer tape allows the temperature sensor to trackthe temperature of the F/T sensor body; it is easy to install thetemperature sensor because there is no cure time; and it reduces theamount of strain the temperature sensor experiences from loading. Afterthe sensor is installed, a protective coating such as silicone RTV (roomtemperature vulcanizing) can be added to protect the sensor and wires.

Similarly to the use of thermal transfer tape, a temperature sensor maybe mounted to the F/T sensor body using epoxy. Epoxy may provide a morerobust connection for high vibration environments, but it at the cost ofincreased installation time and increased strain applied to thetemperature sensor during loading. If the temperature sensor hasuninsulated wires, it may be necessary to apply an insulating layer ofepoxy before the temperature sensor can be installed.

One way to reduce the cost of temperature sensor installation is to usesurface mount temperature sensors on a PCB (printed circuit board) tomeasure the temperature of the F/T sensor body. This may be accomplishedby mounting the surface mount temperature sensor on the bottom of a PCBwhich is mounted to the F/T sensor body, such that the temperaturesensor faces the F/T sensor body. A spacer such as PCB material could beutilized to create a gap between the temperature sensor PCB and the F/Tsensor body, within which the temperature sensor would reside. Thermaltape or paste may be installed in this cavity to allow the temperaturesensor to measure the F/T sensor body temperature, and to allow for sometolerance stackup so the temperature sensor does not need to physicallytouch the F/T sensor body. FIG. 1 depicts an example of this mountingapproach.

As an alternative to creating a cavity using PCB material, a recess maybe milled into the F/T sensor body where the temperature sensor isinstalled.

Categories of Temperature Error

The temperature errors monitored can be classified into threecategories. First is strain gage bias change over temperature. Thisaccounts for strain gage TCR and electronics offset drift. This can alsoaccount for unequal expansion rates of adaptor plates when notemperature gradient is present. Second is gain change over temperature.This accounts for strain gage TCGF, electronics excitation voltagetemperature coefficient, and electronics gain temperature coefficient.The final category is the MAP to TAP temperature gradient. This accountsfor mechanical behavior from a temperature gradient from the sensor'sMAP to the sensor's TAP.

The inventors have developed an analog front-end design that minimizeselectronics-related temperature error. This allowed them to focus on thetemperature compensation of the force/torque sensor itself, since theanalog electronics are much more stable than the temperature sensors.The inventors discovered that the bias change over temperature and gainchange over temperature can both be modeled as a linear curve. Theaccuracy of the linear model varies by the force/torque sensormonitored. However, among all F/T sensors, a more accurate mathematicalmodel is a quadratic curve. The inventors also discovered that the MAPto TAP temperature gradient has a roughly linear relationship to a F/Tsensor's Z-axis force output with a stable temperature gradient and arelatively small temperature difference between MAP and TAP.

Temperature Compensation—Unstrained Strain Gages

Two methods of temperature compensation using unstrained thermal sensorsare bias compensation, and gain compensation.

Bias Compensation—In a quarter bridge temperature sensor topology theunstrained gage will exhibit largely the same temperature behavior asthe load sensing gages. The load sensing gages in a quarter-bridge canbe effectively temperature compensated by subtracting the unstrainedgage voltage from the load sensing gage voltage. This subtraction can beperformed in software or directly by a differential input DAQ or ADC.This effectively creates a pseudo half-bridge circuit that allows aquarter bridge instrumented F/T sensor to have acceptable temperatureperformance. FIG. 2 depicts a representative circuit, in which R1-R3 arefixed bridge completion resistors, SG0 and SG1 are load-sensing straingages, and SGU is an unstrained strain gage (used for temperaturesensing/compensation).

Gain Compensation—Silicon strain gages change sensitivity overtemperature, so gain compensation allows the sensor to maintainsensitivity over wide temperature ranges. This change in sensitivityover temperature is fairly consistent from gage to gage and can bereasonably characterized using a few representative sensors. The basiccompensation math is as followsFT_(compensated) =k·FT_(uncompenstated) wherek=F(G _(unstrained) −G _(unstrained_at_room_temp))  (1)The function in this equation is a simple quadratic fit. The unstrainedgage output is referenced to its output at room temperature to accountfor variance in the bonded resistance of the instrumented strain gage.Using this method, changes in gain can be compensated because gainshould be constant at isothermal points throughout the operating range.

Temperature Compensation—Monitoring Measurement Strain Gage Temperatures

Temperature effects can be compensated on each gage using a matrix thatcombines bias and gain quadratic models along with MAP to TAP gradients.Compensating gages rather than resolved F/T sensor output simplifies thecompensation model by reducing the number of temperature sensors inputto the algorithm. A simple compensation model requires less temperaturecharacterization, making it cheaper and more consistent than a complexmodel.

The equation for a temperature-compensated gage reading is:G _(n-compensated) =C ₀ *G _(n) +C ₁ *T _(n) +C ₂ *T _(n) ² +C ₃ *G _(n)*T _(n) +C ₄ *G _(n) *T _(n) ² +C ₅*(T _(map) −T _(tap))+C ₆*1  (2)where G_(n) is the gage reading for gage n, T_(n) is the temperature ofthe gage, T_(map) is the temperature of the MAP, and T_(tap) is thetemperature of the TAP. Table 1 below maps the compensation equationcoefficients to the terms on which they act:

TABLE 1 Temperature Compensation Equation Coefficients Coefficient C₀ C₁C₂ C₃ C₄ C₅ C₆ Terms G_(n) T_(n) T_(n) ² G_(n)*T_(n) G_(n)*T_(n) ²T_(map)-T_(tap) 1 Comment gain bias sensitivity MAP/TAP constant c forquadrat- ic equation

The resulting compensated gage readings are then multiplied by astandard 6×6 calibration matrix resulting in 6-axis F/T sensor readings.While it is possible to enter all temperature data into the force/torquematrices, this approach is computationally complex. The more optimizedapproach is to temperature-compensate each individual gage, then resolvethe temperature-compensated gage readings to achieve force/torquevalues.

The compensation matrix is calculated, in one embodiment, using a leastsquares algorithm. The least squares algorithm can be given the entiredata set from the characterization tests, or it can be given specificreadings from only the soak points; either method produces comparableresults. One requirement to obtain good results is estimating a correctset of expected gage readings for the least squares algorithm. Each testrequires one data point with the sensor thermally equalized at 22° C.,to know what the gages are supposed to read for that test at differenttemperatures. A constant load should also be applied to the sensorthroughout the test. This allows for arbitrary loads to the sensor foreach characterization test. It is possible to calculate expected gagereadings at 22° C. by extrapolating gage values using the loaded andunloaded temperature swings. This can be useful, with some force/torquesensors, if a test cannot soak at 22° C. See Appendix A for an example,including full thermal sensor data and calculation of the temperaturecompensation coefficients.

Deriving Temperature of Strain Gages from Bridge Current

A primary reason for using a half-bridge or full-bridge circuit topologyto measure strain gage output is to cancel the effect of the largetemperature coefficient of silicon strain gages. By arranging the gagesin a half-bridge or full-bridge circuit, with gages receiving equal andopposite strain from sensor loading, the bridge output voltage changefrom loading is maximized while the bridge output voltage change fromtemperature change is minimized.

One consequence of using a half-bridge or full-bridge circuit topologywith silicon strain gages is that, with a constant voltage excitation,the current through the bridge varies with temperature, while stayingmostly constant with loading. This allows the current through the straingage bridge to indicate a temperature reading. Thus, the same siliconstrain gages can measure both loading and temperature—the temperaturethus derived can be used for temperature compensation of the F/T sensor,as described herein.

One problem with this approach is that it can be difficult to arrangestrain gages so that they actually experience equal and oppositestrains. This strain mismatch causes the bridge current to vary withsensor loading, resulting in an inaccurate temperature calculation.

It has been discovered that it is possible to use the bridge outputvoltage and bridge current to calculate the average bridge temperature,as long as: (1) there are more than one strain sensing elements in thebridge (otherwise the bridge voltage and current would be proportionaland wouldn't provide enough information), and (2) all gages have thesame sign temperature coefficient (large temperature coefficientvariations make this less accurate).

FIG. 3 depicts the circuit configuration for one embodiment. Linear andquadratic combinations of the bridge output voltage and bridge currentare multiplied by a matrix of coefficients to derive average temperaturevalues for the strain gage bridge. These coefficients are derived usinga least squares fit to sensor loading data and sensor temperature data.This math can be simplified by removing terms to reduce the complexityof the characterization process, or additional nonlinear terms could beadded to improve the model's fit. The coefficients are:

TABLE 2 Average Temperature Coefficients Coefficient C₀ C₁ C₂ C₃ C₄ C₅C₆ C₇ Terms V V² V³ I I² V*I V*I² 1

The equation yielding the average bridge temperature is:Temp_(avg) =C0*V+C1*V ² +C2*V ³ +C3*I+C4*I ² +C5*V*I+C6*V*I ² +C7  (3)Of course, in any given implementation, one or more of the coefficientsmay be zero, effectively eliminating the corresponding term fromequation (3).

A Monte-Carlo style simulation of a silicon strain gage bridge showsthat with adequate calibration steps the model above can calculateaccurate temperature data. The simulation creates a set of differentgage combinations where the initial resistance, bond strain, TCR, TCGF,and GF all vary with a normal distribution. For each gage combinationseveral different strain and temperature combinations are applied andeach combination has a least-squares fit to the input temperature. Thegraph of FIG. 4, and the statistics below, show the max/min worst casetemperature error for each gage combination, demonstrating this model isa good fit to silicon strain gage behavior.

Num samples: 2000000

Worst max temp error: 0.089296

Avg max temp error: 0.033637

Std max temp error: 0.008338

Worst min temp error: −0.075849

Avg min temp error: −0.027590

Std min temp error: 0.009062

This calculation still works if one gage in a half-bridge experiencesreduced strain or no strain from loading, because the voltage andcurrent readings still differ significantly between loading andtemperature changes. The compensation coefficients can be derivedwithout knowing the actual strains experienced by the gages; only thetemperature experienced by the gages is important. Using the straingages as their own temperature sensors eliminates any time lag betweenthe strain gages and the temperature measured by the F/T sensor. Usingthe strain gages as their own temperature sensor can be an inexpensivemethod to add temperature sensing or temperature compensation to a F/Tsensor without adding material cost.

Temperature Compensation Experiments

Several experiments were conducted, with a variety of temperaturesensors and various heating and loading conditions.

In one experiment, 17 thermistors were placed in various locations on aparticular force/torque sensor, as indicated in FIG. 5. The F/T sensorinvestigated was an Axia 80 monolithic F/T sensor available from ATIIndustrial Automation, Inc. of Apex, N.C. The Axia 80 F/T sensor hasstrain gages on only the upper surface of each beam connecting the MAPand TAP, as described in US Patent Application Publication No.2017/0205296 (the '296 application), assigned to the assignee of thepresent application and incorporated herein by reference in itsentirety. As indicated in FIG. 1, thermistors 0, 1, and 2 were placeddirectly adjacent strain gages. Fourteen other thermistors were placedin various locations on both the MAP and TAP portions of the sensor. Thethermistors with numbers in circles were placed on the top or side wall;thermistor numbers without circles were placed on the TAP crevice.

In another experiment, two thermistors were placed on a Nano 25 F/Tsensor, available from ATI Industrial Automation, Inc. of Apex, N.C. Asuitable thermistor is the NXFT15XH103FA2B025 available from MurataManufacturing Co., Ltd. of Nagaokakyo, Kyoto, Japan. One thermistor wasaffixed to the MAP, and the other to the TAP, thus providing a MAP/TAPtemperature gradient. The temperatures of individual measurement straingages were not measured or compensated.

All tests were performed with the same aluminum plates attached to theF/T sensor because the F/T sensor is a steel body and the aluminumplates will impart a load on the F/T sensor as they change temperature.Keeping the plates consistent allows this behavior to be compensated.Three tests were performed: unloaded temperature swing, loadedtemperature swing, and MAP/TAP thermal gradient.

F/T sensor unloaded temperature swing—The sensor was placed on the floorof a temperature chamber and run through a 0-50° C. temperature swingwith 3 hour soak points at 0° C., 22° C., and 50° C.

F/T sensor loaded temperature swing—A complex load was applied to thesensor that caused a significant change in all gage outputs. The sensorwas then run through a 0-50° C. temperature swing with 3 hour soakpoints at 0° C., 22° C., and 50° C.

MAP heating applied with TAP heat sink—A large metal plate was attachedto the TAP of the sensor using thermal transfer tape and heat wasapplied to the MAP of the sensor using a hot plate. A thermocouple wasused to ensure the hot plate reached 50° C. near the sensor and the TAPheat sink ensured the TAP stayed cooler than the MAP. The test wasstarted at 22° C. to ensure a room temperature reading with the TAP heatsink was taken.

The temperature compensation equation above was applied to each straingage.

The ordinary least squares algorithm is used to calculate the abovecompensation coefficients using the below test data. The ordinary leastsquares algorithm requires two data sets in order to calculate acompensation matrix: (1) training data for each test, and (2) input ordesired data for each test.

A set of gage and thermistor training data was collected from the soakpoints of each test and at least one sample with a significant MAP toTAP temperature gradient. The data below is in 24-bit counts.

Description G0 G1 G2 G3 G4 G5 TAP MAP 0° C. no load −109275 −202564−27135 −68595 −51450 884 −2105077 −1958071 22° C. no load −119295−210996 −37952 −63898 −60794 −2543 −375038 −175817 50° C. no load−133424 −220075 −50570 −58955 −73105 −7001 1542173 1755958 0° C. load−339596 117263 84603.1 337492 70706.6 235424 −2097453 −1955110 22° C.load −349417 108634 72969.1 342428 60678.2 231572 −376046 −179785 50° C.load −358781 97568.7 58507.1 344845 46288.2 225230 1542387 1756143 22°C. MAP −114823 −203858 −54863 −89834 −57615 −7647 −429929 −265120heating MAP heating 1 −162071 −210788 −108417 −88308 −112375 −15738120871.5 1907875 MAP heating 2 −136118 −207776 −78510 −87715 −81040−11204 291801.4 1106552

The thermistor readings were linearized using the below equations and Bconstant for the thermistor used. Note: The DAQ system introduced asignificant offset error to the thermistor calculations, but this doesnot significantly affect the compensation results.

${vpv} = {\frac{Counts}{2^{23}} + 0.5}$$R = {R_{0}*\frac{1 - {vpv}}{vpv}}$${T( {{^\circ}\mspace{14mu}{C.}} )} = {\frac{B}{\ln( \frac{R}{R_{0}*e^{{- B}\text{/}T_{0}}} )} - 273.15}$where B=3380, R₀=10kΩ, T₀=298.15 K for the specific thermistors used.

TAP MAP Description ° C. ° C. 0° C. no load −1.45 0.56 22° C. no load20.36 22.81 50° C. no load 46.77 50.47 0° C. load −1.34 0.60 22° C. load20.35 22.76 50° C. load 46.78 50.47 22° C. MAP 19.69 21.71 heating MAPheating 1 26.52 53.26 MAP heating 2 28.71 39.92

For each gage, the set of training data for that gage was calculated.For the temperature input, a weighted average between the MAP and TAPtemperature sensors was calculated (for larger sensors, use thetemperature sensor next to the gage). In this case, equal weightingbetween the MAP and TAP was used.T=0.5*T _(MAP)+0.5*T _(TAP)

G0 T ° C. T{circumflex over ( )}2 G0*T G0*T{circumflex over ( )}2MAP-TAP ° C. 1 −109275 −0.44 0.20 48416 −21451 2.02 1 −119295 21.58465.86 −2574841 −55574867 2.45 1 −133424 48.62 2363.81 −6486949−315388878 3.70 1 −339596 −0.37 0.14 125664 −46500 1.95 1 −349417 21.55464.54 −7531009 −162316459 2.42 1 −358781 48.62 2364.14 −17444811−848209002 3.69 1 −114823 20.70 428.35 −2376448 −49184550 2.02 1 −16207139.89 1591.56 −6465736 −257946792 26.74 1 −136118 34.32 1177.71 −4671273−160307578 11.21 1 G1 T ° C. T{circumflex over ( )}2 G1*TG1*T{circumflex over ( )}2 MAP-TAP ° C. 1 −202564 −0.44 0.20 89748−39764 2.02 1 −210996 21.58 465.86 −455104 −98294922 2.45 1 −22007548.62 2363.81 −10699839 −520215330 3.70 1 117263 −0.37 0.14 −43392 160571.95 1 108634 21.55 464.54 2341392 50464218 2.42 1 97569 48.62 2364.144744028 230666115 3.69 1 −203858 20.70 428.35 −4219180 −87322968 2.02 1−210788 39.89 1591.56 −8409263 −335482661 26.74 1 −207776 34.32 1177.71−7130407 −244699512 11.21 1 G2 T ° C. T{circumflex over ( )}2 G2*TG2*T{circumflex over ( )}2 MAP-TAP ° C. 1 −27135 −0.44 0.20 12022 −53272.02 1 −37952 21.58 465.86 −819153 −17680438 2.45 1 −50570 48.62 2363.81−2458674 −119538246 3.70 1 84603 −0.37 0.14 −31306 11585 1.95 1 7296921.55 464.54 1572710 33896746 2.42 1 58507 48.62 2364.14 2844759138319082 3.69 1 −54863 20.70 428.35 −1135472 −23500493 2.02 1 −10841739.89 1591.56 −4325251 −172553358 26.74 1 −78510 34.32 1177.71 −2694270−92461282 11.21 1 G3 T ° C. T{circumflex over ( )}2 G3*T G3*T{circumflexover ( )}2 MAP-TAP ° C. 1 −68595 −0.44 0.20 30392 −13465 2.02 1 −6389821.58 465.86 −1379167 −29767681 2.45 1 −58955 48.62 2363.81 −2866325−139357835 3.70 1 337492 −0.37 0.14 −124885 46212 1.95 1 342428 21.55464.54 7380381 159069957 2.42 1 344845 48.62 2364.14 16767194 8152616043.69 1 −89834 20.70 428.35 −1859269 −38480667 2.02 1 −88308 39.891591.56 −3523010 −140548428 26.74 1 −87715 34.32 1177.71 −3010180−103302588 11.21 1 G4 T ° C. T{circumflex over ( )}2 G4*TG4*T{circumflex over ( )}2 MAP-TAP ° C. 1 −51450 −0.44 0.20 22795 −101002.02 1 −60794 21.58 465.86 −1312168 −28321575 2.45 1 −73105 48.622363.81 −3554280 −172805484 3.70 1 70707 −0.37 0.14 −26164 9682 1.95 160678 21.55 464.54 1307802 28187175 2.42 1 46288 48.62 2364.14 2250643109431735 3.69 1 −57615 20.70 428.35 −1192431 −24679347 2.02 1 −11237539.89 1591.56 −4483142 −178852327 26.74 1 −81040 34.32 1177.71 −2781125−95441960 11.21 1 G5 T ° C. T{circumflex over ( )}2 G5*T G5*T{circumflexover ( )}2 MAP-TAP ° C. 1 884 −0.44 0.20 −392 174 2.02 1 −2543 21.58465.86 −54886 −1184651 2.45 1 −7001 48.62 2363.81 −340385 −16549178 3.701 235424 −0.37 0.14 −87116 32236 1.95 1 231572 21.55 464.54 4991090107573378 2.42 1 225230 48.62 2364.14 10951237 532475670 3.69 1 −764720.70 428.35 −158259 −3275437 2.02 1 −15738 39.89 1591.56 −627857−25048008 26.74 1 −11204 34.32 1177.71 −384487 −13194738 11.21 1

The input data set consists of the gage values the sensor should outputfor each of the above samples in the training data set. In this case,the gages should output the readings at 22° C., with no MAP to TAPthermal gradient present.

Description G0 G1 G2 G3 G4 G5 0° C. no load −119295 −210996 −37952−63898 −60794 −2543 22° C. no load −119295 −210996 −37952 −63898 −60794−2543 50° C. no load −119295 −210996 −37952 −63898 −60794 −2543 0° C.load −349417 108634 72969.1 342428 60678.2 231572 22° C. load −349417108634 72969.1 342428 60678.2 231572 50° C. load −349417 108634 72969.1−342428 60678.2 231572 22° C. MAP −114823 −203858 −54863 −89834 −57615−7647 heating MAP heating 1 −114823 −203858 −54863 −89834 −57615 −7647MAP heating 2 −114823 −203858 −54863 −89834 −57615 −7647

The compensation matrices were calculated using the least squaresalgorithm and the input and training data sets. The least squaresalgorithm will find coefficients for the compensation model thatminimize error between the compensated outputs and the input data set.Since the input data set is an ideal set of sensor data with notemperature-dependent output, the compensated outputs will have greatlyreduced temperature behavior.

Let A denote a matrix containing the training data set for one gage andB denote a matrix containing the input data set for one gage.TempCompMatrix=((A ^(T) *A)⁻¹ *A ^(T) *B)^(T)

MAP-TAP G T° C. T{circumflex over ( )}2 G*T G*T{circumflex over ( )}2 °C. 1 G0 0.998471 474.80 0.61 0.000004 9.79512E−06 1617.86 −13325 G10.999026 388.51 −0.05 −0.000027 3.72456E−06 18.98 −8410 G2 0.994787533.87 −2.01 −0.000669 2.27456E−05 1905.14 −14694 G3 1.000541 −246.091.09 −0.000111  4.734E−06 87.43 4477 G4 0.995720 427.43 −0.44 −0.0005191.97281E−05 1973.10 −13418 G5 0.998033 149.03 0.08 −0.000009 4.50661E−06214.94 −3755

Compensated gage data was calculated from the raw gage readings and thecompensation matrices by multiplying each gage matrix by the transposeof each compensation matrix.G _(comp)=Gage_(matrix)*Comp_(matrix) ^(T)Ex:G0_(comp)=[−291436 −3.14 9.89 916527−2882350 0.042 1]*[1.016102−1653.0731.89−0.002649 6.75E−05 1936.48 15565]^(T)G0_(comp)=−276867

Resolved F/T data was then calculated from the compensated gage datausing a 6×6 linear matrix.

[Fx Fy Fz Tx Ty Tz]=[G0 G1 G2 G3 G4 G5]*(6×6 FT Matrix)^(T)

F/T Sensor Calibration Matrix:

G0 G1 G2 G3 G4 G5 Fx −3.622E−07  1.094E−06  6.459E−06 −1.574E−04−6.279E−06   1.568E−04 Fy −7.498E−06  1.778E−04 −3.255E−06 −9.034E−051.216E−06 −9.203E−05 Fz  3.156E−04 −6.618E−06  3.212E−04 −3.815E−073.237E−04  4.693E−08 Tx −1.852E−08  1.520E−06 −3.195E−06 −7.959E−073.175E−06 −7.782E−07 Ty  3.554E−06 −8.811E−08 −1.871E−06  1.351E−06−1.781E−06  −1.354E−06 Tz  7.215E−08 −1.394E−06  8.726E−08 −1.419E−061.429E−08 −1.444E−06

To verify the compensated F/T sensor's performance, a furthertemperature test was performed. The F/T sensor was mounted in atemperature chamber and soaked at 0° C., 12.5° C., 22° C., 37.5° C., and50° C. With this temperature compensation method, the sensor'stemperature error is brought within 1% of full scale error for thecalibration.

Calibration load ratings: Fxy=125N, Fz=500N, Txyz=3 Nm.

FIG. 6 depicts the uncompensated results, and FIG. 7 depicts temperaturecompensated result, for the three forces and torques (Fx, Fy, Fz, Tx,Ty, Tx). The experiment shows a substantial improvement in Fz driftperformance and good improvement in Fx, Fy, and Ty as well. Tz inparticular did not show much improvement; however, Tz was already below1% FS error before temperature compensation.

Experimental Results

FIGS. 8A-8C depict different treatments of the measurement strain gageoutputs of an Axia 80 force/torque sensor, for each of a series oftests. The tests included unloaded temperature swing; loaded temperatureswing; and both loaded and unloaded MAP to TAP temperature gradient,with heat applied to both the MAP and the TAP.

FIG. 8A depicts these tests with no temperature compensation of themeasurement strain gage outputs. For the unloaded temperatureswing—depicted on the left of FIG. 8A, prior to the first vertical blackline—gage data and temperature sensor data were logged with the sensorunloaded, through a temperature swing of 0-50° C. The test includes fourlong “soak” points—where an applied heating is maintained over time—toensure the entire sensor reaches thermal equilibrium. This test is usedto calibrate the temperature sensors and to compensate bias change overtemperature.

The second graph depicts a loaded temperature swing, in which the sensorwas loaded with a weight on the Fz surface of approximately 50% of theload expected to generate a full scale deflection. The temperature swingis the same as for the unloaded case (four soak points over 0-50° C.).In general, the temperatures may be different, but it is important touse sufficient soak times between temperature changes to ensure theweights come to the same temperature as the sensor body, and are notthermal sinks.

The last two sections of FIG. 8A each depict both loaded and unloadedconditions as heat is applied to only a portion of the sensor. In thethird section, the MAP was heated as a weight was applied to the TAP.The fourth section depicts loaded and unloaded conditions as heat wasapplied to one side of the sensor, i.e., to the TAP.

In all four tests, using quarter bridge topology on the gages, and withno temperature compensation, the Fz reading was useless. The sensoroutput varied over its full range of 900 N (inflection points followingflats in the graph represent changes in applied heat).

FIG. 8B depicts the same test conditions, repeated using temperaturecompensation in the form of an unstrained gage subtraction. As describedin the above-incorporated '296 application, a strain gage similar tothose mounted on the flexible beams is mounted on an unstressed memberof the sensor, and its output is monitored over changes in temperature.FIG. 8 of the '296 application (reproduced here as FIG. 9) depicts amounting point 35 machined into the TAP 12 of a sensor to receive astrain gage for performing temperature compensation. The output of thisunstrained gage is used to compensate the resolved forces and torques,to minimize the influence of strain gage drift over temperature. As FIG.8B indicates, this compensation improves the Fz performance—making itmarginally useful, but still badly out of range, and varying overchanges in temperature and also the rate of heating.

FIG. 8C depicts these test conditions again, in which the abovequadratic compensation equation is applied to each strain gage prior tocombining the gage outputs to resolve the six forces and torques. AsFIG. 8C shows, the Fz force output is dramatically stabilized, over alltest conditions.

Temperature Compensation Method

FIG. 10 depicts the steps of a temperature-compensated method 100 ofoperating a robotic force/torque sensor. The robotic force/torque sensorhas a Tool Adapter Plate (TAP) operative to be connected to a firstobject and a Mounting Adapter Plate (MAP) operative to be connected to asecond object. The force/torque sensor is operative to measure thedirection and magnitude of force and torque between the first and secondobjects. Thermal sensors are attached to the force/torque sensor,measuring at least the MAP and TAP temperatures. Details of thermalsensor mounting are attached hereto as Appendix C.

Initially, outputs of strain gages affixed to members connecting the MAPand TAP, and thermal sensors measuring the temperature of the MAP andTAP, are obtained at a known load and temperature (block 102). Forexample, the sensor may be at 22° C., with no load applied (or a nominalload, such as the weight of a robotic tool attached to the force/torquesensor). The robotic force/torque sensor then undergoes a change intemperature, such as by applying heat in a calibration procedure, orthrough operation, as electronics and the like become exothermic. Straingage and thermal sensor outputs are again obtained after the sensorundergoes the temperature change (block 104). This step may be repeatedseveral times, as the sensor temperature and/or loading changes.Coefficients to a per-gage temperature compensation equation arecalculated, based on the initial gage/thermal sensor outputs and thesame outputs after the temperature change (block 106). In oneembodiment, the coefficients are calculated based on a least-squaresalgorithm, matching the initial and subsequent values to expectedoutputs. Each strain gage output is then temperature compensated, usingthe temperature compensation equation (block 108). In one embodiment,the temperature compensation equation may be that described above withreference to Table 1, using quadratic terms for strain gage bias andgain temperature drift, and a linear term for a MAP-TAP temperaturegradient. In one embodiment, only the MAP-TAP temperature gradient isused (i.e., the other coefficients are zero). Thetemperature-compensated outputs of all strain gages are then combined,according to known techniques, to resolve temperature-compensated forceand torque values (block 110). For example, the '296 application,incorporated above by reference, describes such force/torque processing.

The method 100 may be supplemented in various ways. For example, thebias and gain of strain gages, independent of force/torque loading, overtemperature drift may be accurately estimated by obtaining the output ofa strain gage affixed to a non-stressed member of the force/torquesensor. Such an unstressed member strain gage is described in the '296application, incorporated above by reference.

Transient Temperature Compensation

Temperature compensation according to the first embodiment describedabove is effective at compensating stable temperature gradients, such asa gradient between MAP and TAP. However, there is a significant amountof strain gage output change during transient gradients. A moresophisticated algorithm may be used to compensate for transienttemperature gradients.

In a strain-based force/torque sensor, the goal of transient temperaturecompensation is to be able to predict the temperature at any given pointin the sensing structure. By successfully predicting the temperaturedistribution throughout the sensing structure, the thermally-inducedstrains may also be predicted and removed from the measured signals toremove sensitivity of a F/T sensor to all thermal gradients, whetherthey are steady-state or time-dependent.

Viewed from a differential perspective (similar to how Finite ElementAnalysis would be performed by breaking F/T sensor element up into manysmaller elements), each element of a F/T sensor is part of a thermalcircuit. Each element will also induce some erroneous signal output inthe F/T sensor's readings when that individual element expands orcontracts due to thermal effects. If viewed in matrix form, it can beconsidered that there is a matrix of temperature changes from the F/Tsensor's last bias point where a temperature is recorded for eachelement. This is referred to herein as the temperature matrix. There isalso a matrix of sensitivities that describe the F/T sensor's change inoutput with respect to each element's temperature, which is referred toherein as the temperature sensitivity matrix. These matrices can becombined as follows, denominated as equation (4):

$\lbrack {{Temp}_{1}\cdots\;{Temp}_{n}} \rbrack = {\begin{pmatrix}{{Sensitivity}\mspace{14mu}{of}\mspace{14mu}{Gage}\mspace{14mu} 1\mspace{14mu}{to}\mspace{14mu}{Temp}\mspace{14mu} 1} & \cdots & {{Sensitivity}\mspace{14mu}{of}\mspace{14mu}{Gage}\mspace{14mu} m\mspace{14mu}{to}\mspace{14mu}{Temp}\mspace{14mu} n} \\\vdots & \ddots & \vdots \\{{Sensitivity}\mspace{14mu}{of}\mspace{14mu}{Gage}\mspace{14mu} 1\mspace{14mu}{to}\mspace{14mu}{Temp}\mspace{14mu} n} & \cdots & {{Sensitivity}\mspace{14mu}{of}\mspace{14mu}{Gage}\mspace{14mu} m\mspace{14mu}{to}\mspace{14mu}{Temp}\mspace{14mu} n}\end{pmatrix} = \lbrack {{Gage}\mspace{14mu}{output}\mspace{14mu} 1\mspace{14mu}\cdots\mspace{14mu}{Gage}\mspace{14mu}{output}\mspace{14mu} m} \rbrack}$

This is true of any strain-based sensor which has thermal gradientsacross it. While it is impractical to measure every temperaturethroughout a physical sensor to perform this exact math, it is practicalto design a sensor for the following considerations.

Heat flow is directed by means of insulation or isolation, so itspredominant effects are generated along a finite number of paths. Ifheat flow is not directed along certain paths, then the paths it isallowed to take are routed to areas of the sensing element which have alow sensitivity of relevant gages to temperature changes.

The sensor can be approximated as a finite number of elements, whereeach element has a constant temperature and a single sensitivity ofgages to temperature in this element.

The heat flow through the sensor is governed by the heat equation

$\begin{matrix}{\frac{\partial u}{\partial t}\mspace{14mu}\text{=∝}\mspace{14mu}{\nabla^{2}u}} & (5)\end{matrix}$where u is the temperature as a function of position and time, t istime, x is position, and alpha is the thermal diffusivity of thematerial. Or, more simply in a 1-D approximation:

$\begin{matrix}{\frac{\partial u}{\partial t}\mspace{20mu}\text{=∝}\mspace{14mu}\frac{\partial^{2}u}{\partial x^{2}}} & (6)\end{matrix}$

Equation (6) can be simplified to the following for a differentialelement having a sufficiently small width h (this is the 2^(nd) ordercentral approximation to the second derivative of the temperaturedistribution; other approximations may be used instead):

$\begin{matrix}{\Delta\; u\mspace{14mu}\text{=∝}\mspace{14mu}( \frac{{u( {x + h} )} - {2{u(x)}} + {u( {x - h} )}}{h^{2}} )\Delta\; t} & (7)\end{matrix}$

It can be seen that at steady-state

$( {\frac{\partial u}{\partial t} = 0} )$the second derivative of temperature with respect to position must bezero (assuming no convection, radiation, or internal heat generation),which in turn means that the temperature distribution is simply astraight line across the thermal resistance of the F/T sensor.

Using these two considerations—eq. (7) and the steady-statedistribution—it is possible to determine the temperature at anyarbitrary point in a F/T sensor at any time, and thus compensate out anyerroneous gage signals which are generated by temperature differencesacross the F/T sensor.

In one embodiment, a single temperature sensor is positioned at eitherend of a F/T sensor. The sensor is “biased” at a known steady-statecondition, so that according to the steady-state behavior describedabove, the thermal distribution throughout the entire F/T sensor isknown at this one point in time, as all points between the twotemperature sensors are simply a line between the two measuredtemperatures. This bias point can be used to initialize n virtualtemperature sensors with accurate starting temperatures. From there,steady-state assumptions can be neglected as heatflow through the sensoris governed by the heat equation, which can be approximated at run-timeas equation (7). Using equation (7), the propagation of heat through theF/T sensor can be simulated, and should match the actual temperaturedistribution throughout the F/T sensor to the extent that theassumptions about the F/T sensor are made to be accurate. Thetemperature distribution throughout the F/T sensor can then beaccurately predicted at any time following the initial bias point, andutilized for signal compensation. This equation can also be calibratedon a per-sensor basis to account for variations in the thermaldiffusivity of the material, as well as the effective lengths ofelements or observed heat losses or additions due to convection,radiation, or internal heat generation.

Once the temperature distribution throughout the entire structure isknown at any given time, it is a simple matter subtract out the gageeffects observed by the F/T sensor from the sensor's outputs accordingto equation (4). In addition, the temperature of the gages can bepredicted by this method, and any changes in gage behavior due totemperature effects can be canceled out.

Modifications of the heat equation are readily available which accountfor convection, radiation, and internal heat generation. Those of skillin the art may readily utilize these modifications in this compensationmethod to provide more accurate results, given the teachings of thepresent disclosure.

An arbitrary number of temperature sensors may be used with thismethodology to characterize heat paths which may not be strictlyone-dimensional, or to provide corrections to the 1-D simulation.

Although purely linear equations are described here, it is possible toaccount for changes in young's modulus, the coefficient of thermalexpansion, the thermal diffusivity, and any other properties overtemperature, with additional linear terms or the addition of nonlinearterms. Such modification is well within the skill of those of ordinaryskill in the art, without undue experimentation, given the teachingsherein.

According to this embodiment of temperature compensation, anapproximation of the heat equation is used to predict the totaltemperature distribution in a F/T sensor with a limited input dataset;the derived data is subsequently utilized, in addition to the measureddata, to calibrate a F/T sensor using a regression technique such as,e.g., linear least squares, so the F/T sensor output remains stable overtemperature changes, whether they are steady-state or transient.

The temperature sensors must be placed so that they observe atemperature change before the temperature change causes a change inoutput of the F/T sensor, otherwise not all thermal effects can becancelled out.

As an example, assume a F/T sensor with two strain gages and threevirtual temperature sensors:

[G₀ G₁]=G

[T_(v0) T_(v1) T_(v2)]=T_(v)

If T_(v0) is the temperature of G₀ and an actual temperature sensor T₂(independent of the three virtual temperature sensors) is thetemperature of G₁, then the compensation equations (2) for the two gagesare:G ₀ =C ₀ G ₀ +C ₁ T _(v0) +C ₂ T _(v0) ² +C ₃ G ₀ T ₀ +C ₄ G ₀ T ₀ ² +C₅(T _(map) −T _(tap))+C ₆ +C ₇ T _(v0) +C ₈ T _(v1) +C ₉ T _(v2)G ₁ =C ₁₀ G ₁ +C ₁₁ T ₂ +C ₁₂ T ₂ ² +C ₁₃ G ₁ T ₂ +C ₁₄ G ₁ T ₂ ² +C₁₅(T _(map) −T _(tap))+C ₁₆ +C ₁₇ T ₂ +C ₁₈ T ₂ +C ₁₉ T ₂The last three terms in each gage compensation equation represent thesubtraction of the transient effects according to equation (4) (notethat, in the equation for G₀, the terms C₁T_(v0) and C₇T_(v0) areredundant).

Hence, a modified version of the compensation equation (2), whichaccounts for transient temperatures, is:G _(n-comp) =C ₀ G _(n) +C ₁ T _(n) +C ₂ T _(n) ² +C ₃ G _(n) T _(n) +C₄ G _(n) T _(n) ² +C ₅(T _(map) −T _(tap))+C ₆1+G _(n-transient)  (8)where the last G_(n-transient) is a matrix of compensation terms for thevirtual temperature sensors, derived from equation (4). Another way ofexpressing equation (8) is thus:G _(n-comp) =C ₀ G _(n) +C ₁ T _(n) +C ₂ T _(n) ² +C ₃ G _(n) T _(n) +C₄ G _(n) T _(n) ² +C ₅(T _(map) −T _(tap))+C ₆1+C ₇ T _(v0) + . . . +C_(m+7) T _(vm)where m is the number of virtual temperature sensors simulated by theheat equation model.

Advantages of Embodiments of the Invention

Embodiments of the present invention present numerous advantages overrobotic force/torque sensors known in the prior art. By providingtemperature compensation, the deleterious effects of temperature change,such as changes in strain gage resistance and gain, may be mitigated. Insome embodiments, this enables the use of silicon strain gages, whichare well suited to robotic force/torque sensor application, but for thesignificant temperature-induced errors. On some force/torque sensors,only two thermal sensors are required, as compensating only for theMAP-TAP thermal gradient gives good results. In other applications,thermal sensors placed proximate measurement strain gages provideadditional compensation terms, more accurately removing thermal effectsfrom the resolved force/torque measurements.

The present invention may, of course, be carried out in other ways thanthose specifically set forth herein without departing from essentialcharacteristics of the invention. The present embodiments are to beconsidered in all respects as illustrative and not restrictive, and allchanges coming within the meaning and equivalency range of the appendedclaims are intended to be embraced therein.

What is claimed is:
 1. A temperature-compensated method of operating arobotic force/torque sensor having a Tool Adapter Plate (TAP) operativeto be connected to a first object and a Mounting Adapter Plate (MAP)operative to be connected to a second object, the force/torque sensorbeing operative to measure the direction and magnitude of force andtorque between the first and second objects, the method comprising:obtaining initial outputs of strain gages affixed to members connectingthe MAP and TAP and thermal sensors measuring the temperature of the MAPand TAP, at a known load and temperature; obtaining strain gage andthermal sensor outputs after the sensor undergoes a temperature change;calculating coefficients to a per-gage temperature compensation equationbased on the initial outputs and outputs after the temperature change;compensating each strain gage output using the temperature compensationequation; and combining the temperature-compensated outputs of allstrain gages to resolve temperature-compensated force and torque values.2. The method of claim 1 wherein: the thermal sensors measure a thermalgradient between the MAP and TAP of the robotic force/torque sensor; andthe per-gage temperature compensation equation includes a termrepresenting the MAP-TAP thermal gradient.
 3. The method of claim 2wherein the MAP-TAP thermal gradient term is linear.
 4. The method ofclaim 1 wherein the per-gage temperature compensation equation includesterms representing the temperature of each strain gage.
 5. The method ofclaim 4 wherein the robotic force/torque sensor further includes thermalsensors proximate one or more strain gages, and wherein the thermalsensors indicate the temperature of each strain gage.
 6. The method ofclaim 4 wherein strain gages are connected in a half-bridge orfull-bridge circuit topology, and wherein the temperatures of straingages in each half-bridge or full-bridge circuit are derived from therelationship of current and voltage at the bridge circuit.
 7. The methodof claim 6 wherein the average temperature of strain gages in a bridgecircuit is given by:Temp_(avg) =C0*V+C1*V ² +C2*V ³ +C3*I+C4*I ² +C5*V*I+C6*V*I ² +C7 whereV is the voltage output of the half-bridge or full-bridge circuit, and Iis the current through the half-bridge or full-bridge circuit.
 8. Themethod of claim 4 wherein the per-gage temperature compensation equationincludes terms representing a change in resistance of a strain gage overtemperature and a change in gain of a strain gage over temperature. 9.The method of claim 4 wherein the terms in the per-gage temperaturecompensation equation representing a change in resistance of a straingage over temperature and a change in gain of a strain gage overtemperature are linear.
 10. The method of claim 4 wherein the terms inthe per-gage temperature compensation equation representing a change inresistance of a strain gage over temperature and a change in gain of astrain gage over temperature are quadratic.
 11. The method of claim 1wherein the per-gage temperature compensation equation isG _(n-compensated) =C ₀ *G _(n) +C ₁ *T _(n) +C ₂ *T _(n) ² +C ₃ *G _(n)*T _(n) +C ₄ *G _(n) *T _(n) ² +C ₅*(T _(map) −T _(tap))+C ₆*1 whereG_(a) is the gage reading, T_(n) is the temperature of the gage, T_(map)is the temperature of the MAP, and T_(tap) is the temperature of theTAP.
 12. The method of claim 1 wherein calculating coefficients to aper-gage temperature compensation equation based on the initial outputsand outputs after the sensor undergoes a temperature change comprisescalculating the coefficients using a least squares algorithm.
 13. Themethod of claim 1 further comprising: obtaining outputs from a straingage and associated thermal sensor mounted on an unstressed sensormember; and using the unstressed outputs to track gage outputs overtemperature, independently of loading.
 14. The method of claim 1 whereinthe strain gages are silicon gages.
 15. The method of claim 1 whereinthe thermal sensors are thermistors.
 16. The method of claim 11 whereinthe per-gage temperature compensation equation further includes a matrixof terms associated with virtual temperature sensors, which account fortransient temperatures.
 17. The method of claim 16 wherein the matrix ofterms associated with virtual temperature sensors comprises:$\lbrack {{Temp}_{1}\cdots\;{Temp}_{n}} \rbrack = {\begin{pmatrix}{{Sensitivity}\mspace{14mu}{of}\mspace{14mu}{Gage}\mspace{14mu} 1\mspace{14mu}{to}\mspace{14mu}{Temp}\mspace{14mu} 1} & \cdots & {{Sensitivity}\mspace{14mu}{of}\mspace{14mu}{Gage}\mspace{14mu} m\mspace{14mu}{to}\mspace{14mu}{Temp}\mspace{14mu} n} \\\vdots & \ddots & \vdots \\{{Sensitivity}\mspace{14mu}{of}\mspace{14mu}{Gage}\mspace{14mu} 1\mspace{14mu}{to}\mspace{14mu}{Temp}\mspace{14mu} n} & \cdots & {{Sensitivity}\mspace{14mu}{of}\mspace{14mu}{Gage}\mspace{14mu} m\mspace{14mu}{to}\mspace{14mu}{Temp}\mspace{14mu} n}\end{pmatrix} = \lbrack {{Gage}\mspace{14mu}{output}\mspace{14mu} 1\mspace{14mu}\cdots\mspace{14mu}{Gage}\mspace{14mu}{output}\mspace{14mu} m} \rbrack}$18. A temperature-compensated robotic force/torque sensor comprising: aTool Adapter Plate (TAP) operative to be connected to a first object; aMounting Adapter Plate (MAP) operative to be connected to a secondobject; one or more deformable beams connecting the TAP to the MAP; atleast one strain gage affixed to at least one side of each beam, thestrain gages operative to transduce tensile and compressive forces on asurface of a side of a beam, caused by deformation of the beam, intoelectrical signals; a first thermal sensor affixed to the TAP; a secondthermal sensor affixed to the MAP; and a measurement circuit operativeto measure, in response to electrical signals from all strain gages andtemperature outputs from all thermal sensors, thetemperature-compensated direction and magnitude of force and torquebetween the first and second objects.
 19. The robotic force/torquesensor of claim 18, further comprising a thermal sensor affixedproximate each strain gage.
 20. The robotic force/torque sensor of claim18 wherein the strain gages are silicon gages.
 21. The roboticforce/torque sensor of claim 18 wherein the thermal sensors arethermistors.
 22. The robotic force/torque sensor of claim 18 furthercomprising a strain gage and thermal sensor mounted on an unstressedsensor member.
 23. The robotic force/torque sensor of claim 18 furthercomprising a circuit operative to: calculate coefficients to a per-gagetemperature compensation equation based on initial strain gage andthermal sensor outputs before and after the force/torque sensorundergoes a temperature change; compensate each strain gage output usingthe temperature compensation equation; and combine thetemperature-compensated outputs of all strain gages to resolvetemperature-compensated force and torque values.
 24. The roboticforce/torque sensor of claim 23 wherein the per-gage temperaturecompensation equation includes a term representing the MAP-TAP thermalgradient.
 25. The robotic force/torque sensor of claim 24 wherein theMAP-TAP thermal gradient term is linear.
 26. The robotic force/torquesensor of claim 18 wherein the per-gage temperature compensationequation includes terms representing the temperature of each straingage.
 27. The robotic force/torque sensor of claim 26 wherein therobotic force/torque sensor further includes thermal sensors proximateone or more strain gages, and wherein the thermal sensors indicate thetemperature of each strain gage.
 28. The robotic force/torque sensor ofclaim 26 wherein strain gages are connected in a half-bridge orfull-bridge circuit topology, and wherein the temperatures of straingages in each half-bridge or full-bridge circuit are derived from therelationship of current and voltage at the bridge circuit.
 29. Therobotic force/torque sensor of claim 28 wherein the average temperatureof strain gages in a bridge circuit is given by:Temp_(avg) =C0*V+C1*V ² +C2*V ³ +C3*I+C4*I ² +C5*V*I+C6*V*I ² +C7 whereV is the voltage output of the half-bridge or full-bridge circuit, and Iis the current through the half-bridge or full-bridge circuit.
 30. Therobotic force/torque sensor of claim 26 wherein the per-gage temperaturecompensation equation includes terms representing a change in resistanceof a strain gage over temperature and a change in gain of a strain gageover temperature.
 31. The robotic force/torque sensor of claim 26wherein the terms in the per-gage temperature compensation equationrepresenting a change in resistance of a strain gage over temperatureand a change in gain of a strain gage over temperature are linear. 32.The robotic force/torque sensor of claim 26 wherein the terms in theper-gage temperature compensation equation representing a change inresistance of a strain gage over temperature and a change in gain of astrain gage over temperature are quadratic.
 33. The robotic force/torquesensor of claim 18 wherein the per-gage temperature compensationequation isG _(n-compensated) =C ₀ *G _(n) +C ₁ *T _(n) +C ₂ *T _(n) ² +C ₃ *G _(n)*T _(n) +C ₄ *G _(n) *T _(n) ² +C ₅*(T _(map) −T _(tap))+C ₆*1 whereG_(n) is the gage reading, T_(n) is the temperature of the gage, T_(map)is the temperature of the MAP, and T_(tap) is the temperature of theTAP.
 34. The method of claim 33 wherein the per-gage temperaturecompensation equation further includes a matrix of terms associated withvirtual temperature sensors, which account for transient temperatures.35. The method of claim 34 wherein the matrix of terms associated withvirtual temperature sensors comprises:$\lbrack {{Temp}_{1}\cdots\;{Temp}_{n}} \rbrack = {\begin{pmatrix}{{Sensitivity}\mspace{14mu}{of}\mspace{14mu}{Gage}\mspace{14mu} 1\mspace{14mu}{to}\mspace{14mu}{Temp}\mspace{14mu} 1} & \cdots & {{Sensitivity}\mspace{14mu}{of}\mspace{14mu}{Gage}\mspace{14mu} m\mspace{14mu}{to}\mspace{14mu}{Temp}\mspace{14mu} n} \\\vdots & \ddots & \vdots \\{{Sensitivity}\mspace{14mu}{of}\mspace{14mu}{Gage}\mspace{14mu} 1\mspace{14mu}{to}\mspace{14mu}{Temp}\mspace{14mu} n} & \cdots & {{Sensitivity}\mspace{14mu}{of}\mspace{14mu}{Gage}\mspace{14mu} m\mspace{14mu}{to}\mspace{14mu}{Temp}\mspace{14mu} n}\end{pmatrix} = \lbrack {{Gage}\mspace{14mu}{output}\mspace{14mu} 1\mspace{14mu}\cdots\mspace{14mu}{Gage}\mspace{14mu}{output}\mspace{14mu} m} \rbrack}$36. A temperature-compensated method of operating a robotic force/torque(F/T) sensor having a body with a plurality of strain gages affixed tothe body, and operative to measure the direction and magnitude of forceand torque between first and second objects attached to the F/T sensor,the method comprising: obtaining initial outputs of a plurality ofthermal sensors affixed to the body at first known temperatures and witha known applied load; in response to the initial thermal sensor outputs,modeling a temperature gradient across the F/T sensor body; duringoperation, modeling heat flow through the F/T sensor body by a heatequation, and deriving temperatures of a plurality of points on the F/Tsensor body based on the modeled heat flow; obtaining strain gageoutputs as loads are applied to the F/T sensor; and compensating eachstrain gage output for thermal effects using the derived temperatures ofthe plurality of points on the F/T sensor body based on the modeled heatflow; and combining the temperature-compensated outputs of all straingages to resolve temperature-compensated force and torque values. 37.The method of claim 36, wherein the heat equation is$\Delta\; u\mspace{14mu}\text{=∝}\mspace{14mu}( \frac{{u( {x + h} )} - {2{u(x)}} + {u( {x - h} )}}{h^{2}} )\Delta\; t$where u is the temperature as a function of position and time; t istime, x is position, h is the width of a differential element, and alphais the thermal diffusivity of the F/T sensor body.
 38. The method ofclaim 32 wherein compensating each strain gage output for thermaleffects using the derived temperature of each associated virtual thermalsensor comprises calculating, for each strain gage,G _(n-comp) =C ₀ G _(n) +C ₁ T _(n) +C ₂ T _(n) ² +C ₃ G _(n) T _(n) +C₄ G _(n) T _(n) ² +C ₅(T _(map) −T _(tap))+C ₆1+G _(n-transient) whereG_(n) is the gage reading, T_(n) is the temperature of the gage, T_(map)is the temperature of the MAP, T_(tap) is the temperature of the TAP,and G_(n-transient) is a matrix of compensation terms associated withthe plurality of points on the F/T sensor body based on the modeled heatflow. 39.${{The}\mspace{14mu}{method}\mspace{14mu}{of}\mspace{14mu}{claim}\mspace{14mu} 38\mspace{14mu}{wherein}\mspace{14mu}{the}\mspace{14mu}{matrix}\mspace{14mu} G_{n\text{-}{transient}}\mspace{14mu}{is}\mspace{14mu}{given}\mspace{14mu}{{by}\lbrack {{Temp}_{1}\cdots\;{Temp}_{n}} \rbrack}} = {\begin{pmatrix}{{Sensitivity}\mspace{14mu}{of}\mspace{14mu}{Gage}\mspace{14mu} 1\mspace{14mu}{to}\mspace{14mu}{Temp}\mspace{14mu} 1} & \cdots & {{Sensitivity}\mspace{14mu}{of}\mspace{14mu}{Gage}\mspace{14mu} m\mspace{14mu}{to}\mspace{14mu}{Temp}\mspace{14mu} n} \\\vdots & \ddots & \vdots \\{{Sensitivity}\mspace{14mu}{of}\mspace{14mu}{Gage}\mspace{14mu} 1\mspace{14mu}{to}\mspace{14mu}{Temp}\mspace{14mu} n} & \cdots & {{Sensitivity}\mspace{14mu}{of}\mspace{14mu}{Gage}\mspace{14mu} m\mspace{14mu}{to}\mspace{14mu}{Temp}\mspace{14mu} n}\end{pmatrix} = \lbrack {{Gage}\mspace{14mu}{output}\mspace{14mu} 1\mspace{14mu}\cdots\mspace{14mu}{Gage}\mspace{14mu}{output}\mspace{14mu} m} \rbrack}$40. The method of claim 32 wherein compensating each strain gage outputfor thermal effects using the derived temperature of each associatedvirtual thermal sensor comprises calculating, for each strain gage,G _(n-comp) =C ₀ G _(n) +C ₁ T _(n) +C ₂ T _(n) ² +C ₃ G _(n) T _(n) +C₄ G _(n) T _(n) ² +C ₅(T _(map) −T _(tap))+C ₆1+C ₇ T _(v0) + . . . +C_(m+7) T _(vm) where G_(n) is the gage reading, T_(n) is the temperatureof the gage, T_(map) is the temperature of the MAP, T_(tap) is thetemperature of the TAP, and m is the number of virtual temperaturesensors simulated by the heat equation model.